📐 Maths: Perimeter, Area and Volume

1. In Functional Skills Maths Level 2, which formula gives the perimeter of a rectangle of length l and width w?

1. 2l + 2w
2. l × w
3. l + w
4. l² + w²

The perimeter of a rectangle is the sum of all four sides, which equals 2l + 2w (equivalently 2(l + w)). (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 1 item 22 (rectangle))

2. A rectangular garden bed is 8 m long and 5 m wide. What length of edging is needed to go all the way around its perimeter?

1. 26 m
2. 40 m
3. 13 m
4. 20 m

Perimeter = 2l + 2w = 2(8) + 2(5) = 16 + 10 = 26 m. (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 1 item 22 (rectangle))

3. What is the perimeter of a triangle with side lengths a, b and c?

1. a + b + c
2. (a × b)/2
3. 2(a + b)
4. ½ × b × c

The perimeter of any triangle is simply the sum of its three side lengths, a + b + c. (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 2 item 16 (triangle))

4. A triangular sail has sides measuring 7 m, 9 m and 12 m. What is its perimeter?

1. 28 m
2. 378 m
3. 189 m
4. 32 m

The perimeter of a triangle is the sum of its sides: 7 + 9 + 12 = 28 m. (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 2 item 16 (triangle))

5. A square patio has a side length of 7 m. A builder needs to fit a low wall around its whole perimeter. How long must the wall be?

1. 28 m
2. 49 m
3. 14 m
4. 21 m

For a square the perimeter is 4 × side = 4 × 7 = 28 m (49 m² would be its area, not its perimeter). (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 1 item 22 (square))

6. An L-shaped room is formed by an 8 m by 6 m rectangle with a 3 m by 2 m rectangular corner removed. Going round the outside, the walls measure 8 m, 6 m, 5 m, 4 m, 3 m and 2 m in order. What is the perimeter of the room?

1. 28 m
2. 42 m
3. 48 m
4. 24 m

The perimeter of a composite shape is the total of all its outer edges: 8 + 6 + 5 + 4 + 3 + 2 = 28 m. (DfE 'Subject content: Functional Skills mathematics' (GOV.UK), Level 2 statement 16 (composite shapes))

7. When finding the perimeter of a composite (non-rectangular) shape made from joined rectangles, what should you do?

1. Add together the lengths of every outer edge that bounds the shape
2. Multiply the longest length by the shortest width
3. Split it into rectangles and add their areas
4. Count only the two longest sides

Perimeter is the total distance around the outside, so you add the lengths of all the outer edges; areas are not used for perimeter. (DfE 'Subject content: Functional Skills mathematics' (GOV.UK), Level 2 statement 16 (composite shapes))

8. A rectangular field measures 120 m by 90 m. Fencing costs £8 per metre. What is the total cost of fencing the whole perimeter?

1. £3,360
2. £1,680
3. £86,400
4. £420

Perimeter = 2(120 + 90) = 420 m; cost = 420 × £8 = £3,360. (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 1 item 22 (rectangle))

9. At Functional Skills Maths Level 2, which formulae for 2-D shapes are NOT given in the exam and must be memorised?

1. The triangle and the circle
2. The rectangle and the square
3. The rectangle and the triangle
4. The square and the circle

At Level 2, formulae for 2-D shapes are given except for triangles and circles, which must be known. (DfE 'Subject content: Functional Skills mathematics' (GOV.UK), Level 2 content statement 16)

10. Which formula gives the area of a triangle with base b and perpendicular height h?

1. (b × h) ÷ 2
2. b × h
3. b + h
4. ½ × (b + h)

The area of a triangle is base times perpendicular height divided by two, written as bh/2. (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 2 item 16 (triangle))

11. For a circle of radius r, which pair of formulae is correct?

1. Circumference = 2πr and Area = πr²
2. Circumference = πr² and Area = 2πr
3. Circumference = πr and Area = πr
4. Circumference = πr² and Area = πr²

For a circle of radius r, the circumference is 2πr and the area is πr²; these must be memorised at Level 2. (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 2 item 16 (circle with radius r))

12. At Functional Skills Maths Level 2, the formulae for which 3-D shape are NOT provided and must be memorised?

1. The cylinder
2. The cuboid
3. The cube
4. The sphere

For 3-D shapes, formulae are given except for cylinders, so the cylinder formulae must be known. (DfE 'Subject content: Functional Skills mathematics' (GOV.UK), Level 2 content statement 17)

13. Which formula gives the volume of a cylinder with radius r and height h?

1. πr²h
2. 2πrh
3. πrh
4. 2πr²h

The volume of a cylinder is the circular base area (πr²) multiplied by the height, giving πr²h. (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 2 item 17 (cylinder with radius r))

14. Which formula gives the total surface area of a closed cylinder with radius r and height h?

1. 2πr² + 2πrh
2. πr²h
3. 2πrh
4. πr² + πrh

The total surface area of a closed cylinder is the two circular ends (2πr²) plus the curved side (2πrh). (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 2 item 17 (cylinder with radius r))

15. Which formula gives the volume of a cuboid with length l, width w and height h?

1. l × w × h
2. 2(lw + wh + lh)
3. l + w + h
4. l × w

The volume of a cuboid is length times width times height, lwh. (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 1 item 23 (cuboid))

16. In design and measurement problems, which unit is correct for reporting a volume?

1. Cubic units such as m³ or cm³
2. Square units such as m² or cm²
3. Linear units such as m or cm
4. No units are needed for volume

Volume is a three-dimensional measure, so it is given in cubic units such as m³ or cm³; using the wrong dimension loses marks. (DfE 'Subject content: Functional Skills mathematics' (GOV.UK), Level 2 statements 16–17 (units))

17. A storage cube has a side length of 5 cm. What is its volume?

1. 125 cm³
2. 15 cm³
3. 25 cm³
4. 75 cm³

The volume of a cube is side³ = 5 × 5 × 5 = 125 cm³. (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 1 item 23 (cube))

18. A rectangular kitchen floor measures 6 m by 4 m. What is its floor area?

1. 24 m²
2. 20 m²
3. 10 m²
4. 24 m

Floor area of a rectangle = length × width = 6 × 4 = 24 m², which is a square measure. (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 1 item 22 (rectangle))

19. A floor has an area of 12 m². Square tiles each cover 0.25 m². Assuming no waste, how many tiles are needed to cover the floor?

1. 48
2. 3
3. 24
4. 60

Number of tiles = total area ÷ tile area = 12 ÷ 0.25 = 48 tiles. (DfE 'Subject content: Functional Skills mathematics' (GOV.UK), Level 2 statement 16 (area in design problems))

20. A wall measuring 5 m by 3 m is to be painted. One 5 m by 3 m wall makes 15 m². If there are two such walls, what is the total area to paint?

1. 30 m²
2. 15 m²
3. 45 m²
4. 8 m²

Each wall is 5 × 3 = 15 m², so two walls give 15 × 2 = 30 m². (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 1 item 22 (rectangle))

21. A total wall area of 30 m² must be painted. One tin of paint covers 12 m². How many whole tins must be bought?

1. 3
2. 2
3. 4
4. 30

30 ÷ 12 = 2.5 tins, and you cannot buy half a tin, so you must round up to 3 tins. (DfE 'Subject content: Functional Skills mathematics' (GOV.UK), Level 2 statement 16 (area in painting problems))

22. A storage box is a cuboid measuring 4 m by 3 m by 2 m. What volume of goods can it hold?

1. 24 m³
2. 9 m³
3. 24 m²
4. 12 m³

Volume of a cuboid = l × w × h = 4 × 3 × 2 = 24 m³. (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 1 item 23 (cuboid))

23. A shipping container has internal dimensions 60 cm by 40 cm by 30 cm. Small boxes each measure 20 cm by 20 cm by 15 cm and pack with no gaps. How many small boxes fit inside?

1. 12
2. 6
3. 18
4. 24

Container volume = 60 × 40 × 30 = 72,000 cm³; box volume = 20 × 20 × 15 = 6,000 cm³; 72,000 ÷ 6,000 = 12 boxes. (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 1 item 23 (cuboid))

24. A cylindrical water tank has a radius of 3 m and a height of 10 m. Using π = 3.14, what is its approximate volume?

1. 282.6 m³
2. 94.2 m³
3. 188.4 m³
4. 565.2 m³

Volume of a cylinder = πr²h = 3.14 × 3² × 10 = 3.14 × 9 × 10 = 282.6 m³. (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 2 item 17 (cylinder))

25. A triangular flower bed has a base of 10 m and a perpendicular height of 6 m. What is its area?

1. 30 m²
2. 60 m²
3. 16 m²
4. 30 m

Area of a triangle = (base × height) ÷ 2 = (10 × 6) ÷ 2 = 30 m². (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 2 item 16 (triangle))

26. A patio is a composite shape made from a 10 m by 4 m rectangle with a triangle (base 4 m, perpendicular height 3 m) joined to one end. What is the total area to be paved?

1. 46 m²
2. 52 m²
3. 40 m²
4. 58 m²

Split into parts: rectangle = 10 × 4 = 40 m²; triangle = (4 × 3) ÷ 2 = 6 m²; total = 40 + 6 = 46 m². (DfE 'Subject content: Functional Skills mathematics' (GOV.UK), Level 2 statement 16 (composite shapes, split into known parts))

27. An L-shaped floor is an 8 m by 6 m rectangle with a 3 m by 2 m rectangular corner removed. What is the area to be carpeted?

1. 42 m²
2. 48 m²
3. 54 m²
4. 36 m²

Find the full rectangle then subtract the missing corner: (8 × 6) − (3 × 2) = 48 − 6 = 42 m². (DfE 'Subject content: Functional Skills mathematics' (GOV.UK), Level 2 statement 16 (composite shapes, add/subtract parts))

28. Which formula gives the area of a rectangle with length l and width w?

1. Area = l × w
2. Area = 2l + 2w
3. Area = l + w
4. Area = ½ × l × w

The area of a rectangle is length multiplied by width; 2l + 2w would give its perimeter. (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 1 item 22 (rectangle))

29. A rectangular noticeboard measures 12 cm by 7 cm. What is its area?

1. 84 cm²
2. 38 cm²
3. 19 cm²
4. 42 cm²

Area of a rectangle is length × width, so 12 × 7 = 84 cm². (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 1 item 22 (rectangle))

30. A rectangular lawn measures 12 m by 8 m. Turf costs £2.50 per square metre. What is the total cost of turfing the lawn?

1. £240.00
2. £96.00
3. £100.00
4. £480.00

The area is 12 × 8 = 96 m², and 96 × £2.50 = £240.00. (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 1 item 22 (rectangle))

31. A rectangle has an area of 48 cm² and a length of 8 cm. What is its width?

1. 6 cm
2. 40 cm
3. 16 cm
4. 12 cm

Since area = length × width, width = area ÷ length = 48 ÷ 8 = 6 cm. (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 1 item 22 (rectangle))

32. A square has a side length of x. Which expression gives its area?

1. x²
2. 4x
3. 2x
4. x³

A square is a rectangle with equal sides, so its area is x × x = x²; 4x gives the perimeter. (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 1 item 22 (square))

33. A kitchen floor measures 6 m by 4 m. It is tiled with square tiles measuring 0.5 m by 0.5 m. How many tiles are needed to cover the floor exactly?

1. 96
2. 48
3. 24
4. 120

The floor area is 24 m² and each tile is 0.25 m², so 24 ÷ 0.25 = 96 tiles. (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 1 item 22 (rectangle))

34. At Functional Skills Level 2, the formula for the area of a triangle is one you must memorise because it is not provided. Which is correct, where b is the base and h is the perpendicular height?

1. Area = (b × h) ÷ 2
2. Area = b × h
3. Area = b + h
4. Area = 2 × b × h

The area of a triangle is base times perpendicular height, divided by two; this formula is not given in the exam. (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 2 item 16 (triangle))

35. A triangle has a base of 10 cm and a perpendicular height of 6 cm. What is its area?

1. 30 cm²
2. 60 cm²
3. 16 cm²
4. 32 cm²

Area = (base × height) ÷ 2 = (10 × 6) ÷ 2 = 30 cm². (Pearson Edexcel 'Formula for Level 1 & 2 | Functional Skills Mathematics', Level 2 item 16 (triangle))